Cherry Creek High School Summer Assignment

Welcome to Algebra! Please have the following worksheets completed and ready to be handed in on the first day of class in the Fall. Make sure you show your work where appropriate. Answers are provided at the end of the packet for you to check yourself as you work; however, you will not be given credit if you do not show work on problems that require it. It is expected that you have a good understanding of this material coming into these courses, as teachers will not be doing an extensive review of previously learned material. Have a great summer and we look forward to seeing you in the Fall! The CCHS Math Department

Order of Operations & Algebraic Expressions Name ___________________ CCHS Algebra 1 Summer Packet – Worksheet 1 Date _____________ Per ___ Write an algebraic expression for each of the following verbal phrases:

1) Three times a number plus by seven. 2) The product of fourteen and a number.

3) Eight subtracted from five times a number. 4) Nine more than twice a number.

5) The sum of twenty and a number. Use order of operations (PEMDAS) to simplify each of the following expressions. Do NOT use a calculator. SHOW ALL WORK!

6) (18 – 6 ⋅ 2) + 23 ÷ (5 – 1) 7) 7 + 3 ⋅ 24 ÷ 6 8) 50 – 10(4 – 2) + 6

9) [9(5 + 3)] – 144 10) 8 ⋅ 22 + 7(4 + 1) 11)

!

2 "7 + 26

16#3 "22

12) (102 – 4 ⋅ 8) ÷ (8 + 9) 13) 17 – 52 ÷ (24 + 32) Evaluate each expression for x = 5, y = -2, z = 1. Do NOT use a calculator:

14) xyz 15) x + y – 12 16) -4y – x 17)

!

4x

y

Simplify without the aid of calculator:

18) – 7 – (-6) 19)

!

21

3+ 3

1

6 20) – 30 + 54

21) – 45 + -22 22)

!

"12

3 23) (-4)(-7)

Simplify each expression. Use the distributive property and combining like terms: 24) 2(3x + 2) 25) –(x – 7) 26) 2(4 + y) + 20 27) 5(t – 3) – 2t 28) -2(3 + d) + 8d – 2 29) 4(2a + 2) – 17

Solving Linear Equations Name ___________________ CCHS Algebra 1 Summer Packet – Worksheet 2 Date _____________ Per ___ Solve each of the following equations for the given variable. SHOW ALL WORK, and remember to check your answers:

1) x + 5 = 12 2) z – 6 = -19 3) 3c = -63

4)

!

y

6= 4 5)

!

2

3x = 8 6) –x + 4 = -7

7) -2z + 1 = -9 8) 4x - 12 = 11 9)

!

x

3"5 = "1

10) 30 = 16 +

!

x

5 11) -7x + 4x = 9 12) 3(x – 2) = 18

13) 3x – 7 + x = -13 14) 4x + 2 = 3x + 7 15) 6x + 5 = 3x + 14 16) 5(4 + 4x) = 12x + 12 17) 6x + 12 – x = 62 18) -4(x – 3) = -x

Write an equation to model each situation below and then solve. Do not forget to put units on your answer if they are needed:

19) You are shopping and have $20 to spend on a birthday present for your brother. You know he loves baseball cards, which are $1.50 a piece. You have already spent $3.50 on a card and wrapping paper. How many baseball cards can you buy your brother? 20) The sum of Kent’s and Lesley’s ages is 53. If Kent is 26, how old is Lesley? 21) You started the school day with some money in your pocket. All you spent was $4.65 on lunch. You now have $7.39 in your pocket. How much money did you initially bring to school? 22) Negative 12 times a number is -156. Find the number.

Number Sense – Integers, Fractions, Decimals Name ___________________ CCHS Algebra 1 Summer Packet – Worksheet 3 Date _____________ Per ___ Complete each of the following statements using

!

> , < , or = :

1) 4 ___ -2 2) -6 ___ -5 3) -5 ___ -6 4) 2.4 ___ 5

12

5) 5.1 ___ 5.01 6) -3.2 ___ 6.12 •! 7) -22 ___ -0.2 8) 2.8 ___ 2.79

9) -2 ___

!

"4

2 10) -2.5 ___

!

5

2 11) )7.21.6( ! ___

!

17

5 12) 4 ___

!

15

4

Write each set of the following numbers in increasing order:

13) 3, 1, 5 14) 0, -2, 4 15) -5, -3, -6 16) 2, -4, 0

17) 2.5, -1.5, -1 18)

!

3

4, "

1

3, 5 19)

!

"1

2, "

3

4, "2, "

5

4

20) 3.5, -2.4, -1.8, 0.9 21)

!

"4, "5

4, "

4

5, " 1.5 22)

!

"1

3, " 0.5, "3, "

3

5

23)

!

3

2, "

11

4, "

3

4, "

9

4 24)

!

"1.62, 1.8, 1.75,9

4, " 1.7, "

5

2

Evaluate each of the following expressions:

25) |-8| 26) |4| 27)

!

1

2

28) |-2.3| 29)

!

2

3 30) |1.8|

Use a percent equation or the proportion

!

x

100=

is

of to answer each question below:

31) What is 45% of 180? 32) What is 20% of 85?

33) What percent of 50 is 45? 34) What percent of 5 is 4?

Convert each of the following fractions into decimals without the aid of a calculator:

35)

!

1

2 36)

!

2

5 37)

!

5

8 38)

!

1

4

39)

!

5

4 40)

!

4

4 41)

!

7

5 42)

!

11

4

Convert each of the following decimals into fractions without the aid of a calculator:

43) 0.6 44) 1.25 45)

!

0.33 46) 2.5

Convert each of the following decimals into percentages without the aid of a calculator:

47) 0.6 48) 1.25 49)

!

0.33 50) 2.5

Convert each of the following fractions into percentages without the aid of a calculator:

51)

!

1

2 52)

!

5

8 53)

!

7

5 54)

!

3

3

55) Sixty percent of the people at the Twilight movie premier were female. How many of the 95 people at the theatre were female? *Don’t forget units!*

56) Eighty percent of the class owns at least one pet. If 20 students own a pet, how many total students are in the class? *Don’t forget units!*

57) Rita has been on 12 rides so far at the carnival. If there are 16 rides, what percent of the rides has Rita been on? 58) A math test has 20 problems. You answered 16 problems correctly. What was your test grade as a percent?

x y0 11 32 53 6

x y-2 10 22 34 4

Linear Functions Name ___________________ CCHS Algebra 1 Summer Packet – Worksheet 4 Date _____________ Per ___ 1) Identify the y-intercept of each of the following functions:

A)

!

y = x " 4 B)

!

y = "2

3x + 6 C)

!

x = 8

2) Identify the y-intercept of the function represented in the table below:

3) What is the x-intercept of

!

y =1

2x "2?

4) Find the slope of the line that contains the points in the following table:

5) Identify the slope of the following lines, and determine if the line is increasing, decreasing, horizontal, or vertical. Explain WHY:

A) B)

!

y = 7 C)

!

y = 2x "5

2

6) Courtney plans to rent a car. The car costs $125 per week, plus $0.18 per mile. Write an equation that represents a relationship between the number of miles, M, and the total cost in dollars, D, for a 3-week rental.

7) Thomas charges a customer of his computer repair company $55 for parts and $35 for each

hour he worked. The bill totaled $280. About how long did A.J. work? *Don’t forget units!* 8) Suppose you are helping to prepare a large meal. You can peel 2 carrots per minute. You need

a total of 60 peeled carrots for the recipe. How long will it take you to finish if you have already peeled 18 carrots? *Don’t forget units!*

9) Bonnie and Clyde are renting a canoe at a park. The rental company charges $5 per hour for

the canoe, plus $2 for each life jacket, and it is required for each person to wear a life jacket. If the total cost for their adventure is $41, for how many hours did Bonnie and Clyde rent the canoe? *Don’t forget units!*

10) Two angles are supplementary if the sum of their measures is 180°. ∠A and ∠B are supplementary angles. The measure of ∠A is 109°. What is the measure of ∠B? *Don’t forget units!*

!

A = ( , )

!

B = ( , )

Quadrant: Quadrant:

!

C = ( , )

!

D = ( , )

Quadrant: Quadrant:

!

E = ( , )

!

F = ( , )

Quadrant: Quadrant:

!

G = ( , )

!

H = ( , )

Quadrant: Quadrant:

!

I = ( , )

!

J = ( , )

Quadrant: Quadrant:

Graphing Points and Equations of Lines Name ___________________ CCHS Algebra 1 Summer Packet – Worksheet 5 Date _____________ Per ___ Plot each of the given points on the graph provided. Make sure you label your axes, as well as each of the points on the graph using the appropriate letter:

1)

!

A = (3, 4)

!

B = (0, 2)

!

C = ("3, 5)

!

D = ("4, 0)

!

E = ("6, "5)

!

F = (7, "2)

!

G = (0, 0)

!

H = ("5, 1)

!

I = (0, "8)

!

J = (3, 0) 2) On the graph below, 10 points are plotted. State the coordinate pair for each AND the quadrant in which the point is located:

E

A B

C

D

F

G

H

I J

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

11

3) Write the equation of the following linear function in slope-intercept form:

4) Write the equation of the line that passes through the points (3, 4) and (9, 10). Graph each of the following linear functions on the graphs provided. Be sure to label your axes:

5)

!

y = 2x + 1 6)

!

y = "1

3x "3

7)

!

y =1

4x " 4 8)

!

y =2

3x

ANSWERS TO ALGEBRA 1 SUMMER PACKET

WORKSHEET 1:

1)

!

3x + 7 2)

!

14x 3)

!

5x "8 4)

!

2x + 9 5)

!

20 + x 6) 8 7) 15 8) 36 9) -72 10) 67 11) 10 12) 4 13) 16 14) -10

15) -9 16) 3 17) -10 18) -1 19)

!

11

2 OR 5.5 20) 24

21) -67 22) -4 23) 28 24)

!

6x + 4 25)

!

"x + 7 26)

!

2y + 28 27)

!

3t " 15 28)

!

6d "8 29)

!

8a "9 WORKSHEET 2:

1)

!

x = 7 2)

!

z = "13 3)

!

c = "21 4)

!

y = 24 5)

!

x = 12 6)

!

x = 11 7)

!

z = 5

8)

!

x =23

4 OR 5.75 9)

!

x = 12 10)

!

x = 70 11)

!

x = "3 12)

!

x = 8

13)

!

x = "3

2 OR -1.5 14)

!

x = 5 15)

!

x = 3 16)

!

x = "1 17)

!

x = 10 18)

!

x = 4

19) 11 baseball cards 20) 27 years old 21) $12.04 22) 13 WORKSHEET 3:

1) > 2) < 3) > 4) = 5) > 6) = 7) < 8) > 9) = 10) < 11) = 12) > 13) 1, 3, 5 14) -2, 0, 4

15) -6, -5, -3 16) -4, 0, 2 17) -1.5, -1, 2.5 18)

!

"1

3,

3

4, 5

19)

!

"2, "5

4, "

3

4, "

1

2 20) -2.4, -1.8, 0.9, 3.5 21)

!

"4, " 1.5, "5

4, "

4

5

22)

!

"3, "3

5, "

1

3, " 0.5 23)

!

"11

4, "

9

4, "

3

4,

3

2 24)

!

"5

2, " 1.7, " 1.62, 1.75, 1.8,

9

4

25) 8 26) 4 27)

!

1

2 28) 2.3 29)

!

2

3 30) 1.8 31)

!

x = 81

32)

!

x = 17 33)

!

x = 90% 34)

!

x = 80% 35) 0.5 36) 0.4 37) 0.625

38) 0.25 39) 1.25 40) 1 41) 1.2 42) 2.75 43)

!

3

5 44)

!

5

4

45)

!

1

3 46)

!

5

2 47) 60% 48) 125% 49) 33% 50) 250% 51) 50%

52) 62.5% 53) 120% 54) 100% 55) 57 people 56) 25 students 57) 75% 58) 80%

WORKSHEET 4:

1) A: (0, -4) B: (0, 6) C: none 2) (0, 1) 3) (4, 0) 4)

!

m =1

2

5) A:

!

m = "1

6; decreasing because as y decreases, x increases.

B:

!

m = 0; horizontal because there is no change in y as x increases.

C:

!

m = 2; increasing because as y increases, so does x. 6)

!

D = 0.18M + 125 7) approximately 6.43 hours 8) 21 minutes 9) 7.4 hours 10) m∠B = 71° WORKSHEET 5: 1)

2) A = (2, 3), Q1 B = (-4, 2), Q2 C = (-2, -1), Q3 D = (0, 7), y-axis E = (4, -6), Q4 F = (6, -2), Q4 G = (8, 0), x-axis H = (-7, 7), Q2 I = (0, -7), y-axis J = (-7, -6), Q3

3)

!

y = 2x + 1 4)

!

y = x + 1 5) 6)

WORKSHEET 5 ANSWERS - continued:

7) 8)